HIPERLAN/2 and IEEE 802.11a WLANs support packetized data transmission at a high rate up to 54 Mbps. Details of their physical layers can be found in the relevant specifications: ETSI, ETSI TS 101 475 V. 1.2.2 (2001-02), 2001; IEEE Computer Society, IEEE Std 802.11a-1999, 30 Dec. 1999. In both types of WLANs, orthogonal frequency division multiplexing (OFDM) is used as the modulation technique.
For IEEE 802.11a WLANs, a 16 μs preamble is inserted at the beginning of each data packet. The preamble is divided into two subpreambles. The first one consists of ten identical, short OFDM symbols each having a length of 800 ns. The second one comprises two long OFDM symbols each of length 3.2 μs preceded by a 1.6 μs cyclic prefix. The first subpreamble is used for initial detection of the signal, automatic gain control, diversity selection, coarse frequency-offset compensation and timing synchronization. The second one enables channel estimation and fine frequency-offset compensation. Both subpreambles are shaped by the raised-cosine window. The preamble structure for HIPERLAN/2 is similar to that for IEEE 802.11a WLANs with the exception that (a) the rectangular window is used instead of the raised-cosine window; and (b) the last short training symbol in HIPERLAN/2 is inverted.
To establish timing synchronization, the receiver detects the end of the first subpreamble. This time reference enables the receiver to locate the time instant in the second subpreamble at which the FFT window for fine frequency-offset compensation begins. To detect the end of the first subpreamble, the receiver can correlate the received signal with the short OFDM symbol. The presence of a correlation peak indicates that the first subpreamble has not passed while the absence of an expected correlation peak is an indication that the current time position is in the second subpreamble.
To detect the various preambles and establish timing the receiver has to perform rapid synchronization, e.g., with a correlator. The specifications recommend, though not mandate, a sampling rate of 20 MHz in the digital implementation of the correlator. When a signal arrives at a receiver in IEEE 802.11a WLANs or HIPERLAN/2, the received signal is filtered and downconverted to the baseband frequency. The baseband signal contains two components: the in-phase and quadrature-phase components. The two components are digitized by one or more analog-to-digital converters with a sampling rate set at 20 MHz. Often these two components are represented by a single quantity that is a complex number, wherein the real and imaginary parts of the complex number are the in-phase and quadrature-phase components, respectively.
A sliding correlator is used to process the received signal samples, and generates outputs at a rate of 20 MHz. Since typically 16 complex multiplications are involved in the generation of one correlator output Ξn, and since the correlator outputs are preferably generated at a rate of 20 MHz, it follows that the correlator needs to perform 320 million complex multiplications per second. Not surprisingly, the implementation of the sliding correlator is very complex in view of the demanding number of involved multiplications, which are further described next.
For instance, if rn be the nth complex-valued received signal sample after downconversion and digitization, then the nth correlator output, Ξn, is given by
      Ξ    n    =            ∑              m        =        1            16        ⁢                  r                  n          -          16          +          m                    ⁢              h        m            wherein the sequence of correlator coefficients hm's constitutes the waveform of a short OFDM symbol. Note that Ξn comprises the real and imaginary parts. According to the IEEE 802.11a specification and the HIPERLAN/2 specification, the (complex-valued) waveform of a short OFDM symbol, s(t), is given by
      s    ⁡          (      t      )        =            ∑              k        =                  -          26                    26        ⁢                  S        k            ⁢              ⅇ                  ⅈ2π          ⁢                                          ⁢          k          ⁢                                          ⁢                      Δ            f                    ⁢          t                    wherein Df=312.5 kHz, and S−26:26=√{square root over (13/6)}{0, 0, 1+i, 0, 0, 0, −1−i, 0, 0, 0, 0, 0, 0, −1−i, 0, 0, 0, −1−i, 0, 0, 0, 1+i, 0, 0, 0, 0, 0, 0, 0, −1−i, 0, 0, 0, −1−i, 0, 0, 0, 1+i, 0, 0, 0, 1+i, 0, 0, 0, 1+i, 0, 0, 0, 1+i, 0, 0}. In the above, i is the square root of −1. A convenient choice of hm is hm=(52)−1/2 s(mTsam) where Tsam=50 ns, so that H1:16={−1.1755−0.0208i, −0.1196+0.6969i, 1.2670+0.1123i, 0.8165+0.0000i, 1.2670+0.1123i, −0.1196+0.6969i, −1.1755−0.0208i, 0.4082−0.4082i, 0.0208+1.1755i, −0.6969+0.1196i, −0.1123−1.2670i, −0.8165i, −0.1123−1.2670i, −0.6969+0.1196i, 0.0208+1.1755i, 0.4082−0.4082i}.
In other signal processing applications, primarily in implementing digital filters, there have been attempts at performing filtering without the need to perform multiplication. However, these strategies are tailored for particular applications and, consequently, are not readily applicable to perform multiplierless correlations in the context of in HIPERLAN/2 or IEEE 802.11a WLANs specifications. Some example attempts in the context of multiplierless realization of filters include: D. E. Borth in U.S. Pat. No. 4,775,851 entitled “Multiplierless decimating low-pass filter for a noise-shaping A/D converter,” issued Oct. 4, 1988 and assigned to Motorola, Inc., Schaumburg, Ill.; A. Miron and D. Koo in U.S. Pat. No. 4,791,597 entitled “Multiplierless FIR digital filter with two to the Nth power coefficients,” issued Dec. 13, 1988 and assigned to North American Philips Corporation, New York, N.Y.; K. Lin in U.S. Pat. No. 5,287,299 entitled “Method and apparatus for implementing a digital filter employing coefficients expressed as sums of 2 to an integer power,” issued Feb. 15, 1994 and assigned to Monolith Technologies Corporation, Tucson, Ariz.; and D. Lipka in U.S. Pat. No. 6,202,074 entitled “Multiplierless digital filtering,” issued Mar. 13, 2001 and assigned to Telefonaktiebolaget LM Ericsson, Stockholm, SE.
The aforementioned attempts at realizing multiplierless filters do not teach or suggest fast sliding correlators implementions suitable for in HIPERLAN/2 or IEEE 802.11a WLANs compliant applications.